Abstract:
We model Pup Matching, the logistics problem of matching or pairing semitrailers known as pups to cabs able to tow one or two pups simultaneously, as an NP-complete version of the Network Loading Problem (NLP). We examine a branch and bound solution approach tailored to the NLP formulation through the use of three families of cutting planes and four heuristic procedures. Theoretically, we specify facet defining conditions for a cut family that we refer to as odd flow inequalities and show that each heuristic yields a 2-approximation. Computationally, the cheapest of the four heuristic values achieved an average error of 1.3% among solved test problems randomly generated from realistic data. The branch and bound method solved to optimality 67% of these problems. Application of the cutting plane families reduced the average relative difference between upper and lower bounds prior to branching from 18.8% to 6.4%.
